Brother,
You are not broken because your gifting is not one-on-one evangelism any more than a different brother is not broken becuase he is not gifted to preach.
It may be comforting to know that many preachers are quiet men in their personal lives. I remember overhearing a post-conference conversation with Henry Blackaby where he stated to the attendee that he was a very shy man. (And this brother has preached in filled baseball stadiums!) The same is true of Richard Owen Roberts; very quiet.
I'm glad you mentioned that your wife is quite outgoing. It is not uncommon for one spouse to be more extroverted than the other. Let me guess; you probably enjoying reading and studying don't you? There are certain common threads amongst the various personality types.
If you feel a burden to witness to a particular soul, then pray for God's grace and follow the Spirit's leading but don't fret because this type of ministry is not your strong suite; it is simply how God has made you. Exercise your gifts and bring Him glory. You will find a lot of peace and comfort simply being who God made you to be.
Blessings on your preaching and music outreach!
Grace and peace,
Matthew